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ELECTRON-ELECTRON INTERACTION
By Prof. L. Kaliambos (Natural Philosopher in New Energy) August 4 , 2015 According to the well-established law of Coulomb two electrons of charge (-e) at a distance r exert an electric repulsion Fe given by Fe = Ke2/r2 . However in quantum mechanics under the discovery of the electron spin by Uhlenbeck and Gousmit (1925) one sees that two electrons of opposite spin at very short distances are coupled because the peripheral velocity is greater than the speed of light. (Faster than light). Under this condition in 2008 I published my paper "Spin-spin interactions of electrons and also of nucleons create atomic molecular and nuclear structures" In that paper I showed that in the Helium atom the two electrons of opposite spin exert stronger magnetic attraction than the electric repulsion and behave like one particle with a charge equal to -2e. However the physicists Heisenberg and Dirac (1926) assuming that such an enormous velocity invalidates the wrong relativity, (EXPERIMENTS REJECT EINSTEIN). they abandoned the natural laws of electromagnetism and introduced a qualitative approach called “Exchange Interaction”. For example in the "Exchange Interaction-WIKIPEDIA” one reads: “In physics, the exchange interaction is a quantum mechanical effect between identical particles. (Actually, one should better speak only of the exchange energy, or the exchange term, to avoid the incorrect idea that this effect corresponds to a classical force or potential.) The effect is due to the wave function of indistinguishable particles being subject to exchange symmetry, that is, either remaining unchanged (symmetric) or changing its sign (antisymmetric) when two particles are exchanged.” On the other hand it is indeed unfortunate that such qualitative approaches could not explain the ground state energy of the simplest helium atom. For example in the "Helium atom-WIKIPEDIA” one reads: “A helium atom is an atom of the chemical element helium. Unlike for hydrogen, a closed-form solution to the Schrödinger equation for the helium atom has not been found." Indeed, despite the enormous success of the Bohr model and the quantum mechanics of Schrodinger based on the well-established laws of electromagnetism in explaining the principal features of the hydrogen spectrum and of other one-electron atomic systems, so far, under the abandonment of natural laws neither was able to provide a satisfactory explanation of the two-electron atoms. In atomic physics a two-electron atom is a quantum mechanical system consisting of one nucleus with a charge Ze and just two electrons. This is the first case of many-electron systems. The first few two-electron atoms are: Z =1 : H- hydrogen anion. Z = 2 : He helium atom. Z = 3 : Li+ lithium atom anion. Z = 4 : Be2+beryllium ion. Z = 5 : B3+ boron. Prior to the development of quantum mechanics, an atom with many electrons was portrayed like the solar system, with the electrons representing the planets circulating about the nuclear “sun”. In the solar system, the gravitational interaction between planets is quite small compared with that between any planet and the very massive sun; interplanetary interactions can, therefore, be treated as small perturbations. However, In the helium atom with two electrons, the interaction energy between the two spinning electrons and between an electron and the nucleus are almost of the same magnitude, and a perturbation approach is inapplicable. In 1925 the two young Dutch physicists Uhlenbeck and Goudsmit discovered the electron spin according to which the peripheral velocity of a spinning electron is greater than the speed of light. Since this discovery invalidates Einstein’s relativity it met much opposition by physicists including Pauli. Under the influence of Einstein’s invalid relativity physicists believed that in nature cannot exist velocities faster than the speed of light. So great physicists like Pauli, Heisenberg, and Dirac abandoned the natural laws of electromagnetism in favor of wrong theories including qualitative approaches under an idea of symmetry properties between the two electrons of opposite spin which lead to many complications. Under this physics crisis in 1993 in Olympia I presented at the international conference “Frontiers of fundamental physics” my paper “Impact of Maxwell’s equation of displacement current on electromagnetic laws and comparison of the Maxwellian waves with our model of dipolic particles ", according to which LAWS AND EXPERIMENTS INVALIDATE FIELDS AND RELATIVITY . At the same time in Larissa I tried to find not only the nuclear force and structure but also the coupling of two electrons under the application of the abandoned electromagnetic laws. For example in the photoelectric effect the absorption of light contributed not only to the increase of the electron energy but also to the increase of the electron mass because the particles of light have mass m = hν/c2 . ( See my DISCOVERY OF PHOTON MASS ). However the electron spin which gives a peripheral velocity greater than the speed of light cannot be affected by the photon absorption. Thus after 9 years I presented at the 12th symposium of the Hellenic nuclear physics society my paper “Nuclear structure is governed by the fundamental laws of electromagnetism (NCSR “Demokritos, 2002), and I showed not only my DISCOVERY OF NUCLEAR FORCE AND STRUCTURE but also that the peripheral velocity (u >> c) of two spinning electrons with opposite spin gives an attractive magnetic force Fm stronger than the electric repulsion Fe when the two electrons of mass m and charge (-e) are at a very short separation r < 578.8 /1015 m. Because of the antiparallel spin along the radial direction the interaction of the electron charges gives an electromagnetic force Fem = Fe -Fm . Therefore in my research the integration for calculating the mutual Fem led to the following relation: Fem = Fe - Fm = Ke2/r2 - (Ke2/r4)(9h2/16π2m2c2) Of course for Fe = Fm one gets the equilibrium separation ro = 3h/4πmc = 578.8/1015 m. That is, for r < 578.8/1015 m the two electrons of opposite spin exert an attractive electromagnetic force, because the attractive Fm is stronger than the repulsive Fe . Here Fm is a spin-dependent force of short range. As a consequence this situation provides the physical basis for understanding the pairing of two electrons described qualitatively by the Pauli principle, which cannot be applied in the simplest case of the deuteron in nuclear physics, because the binding energy between the two spinning nucleons occurs when the spin is not opposite (S=0) but parallel (S=1). According to the experiments in the case of two electrons with antiparallel spin the presence of a very strong external magnetic field gives parallel spin (S=1) with electric and magnetic repulsions given by Fem = Fe + Fm So according to the well-established laws of electromagnetism after a detailed analysis of paired electrons in two-electron atoms I concluded that at r < 578.8/1015 m a motional EMF produces vibrations of paired electrons. Unfortunately today physicists in the absence of a detailed knowledge believe that the two electrons of two-electron atoms under the Coulomb repulsion between the electrons move not together as one particle but as separated particles possessing the two opposite points of the diameter of the orbit around the nucleus. In fact, the two electrons of opposite spin behave like one particle circulating about the nucleus under the rules of quantum mechanics forming two-electron orbitals in helium, beryllium etc. In my paper “Spin-spin interaction of electrons and also of nucleons create atomic molecular and nuclear structures” published in Ind. J. Th. Phys. (2008) I showed that the positive vibration energy (Ev) described in eV depends on the Ze charge of nucleus as Ev = (16.95)Z - 4.1 Of course in the absence of such a vibration energy Ev it is well-known that the ground state energy E described in eV for two orbiting electrons could be given by the Bohr model as E = (-27.2) Z2. So the combination of the energies of the Bohr model and the vibration energies due to the opposite spin of two electrons led to my discovery of the ground state energy of two-electron atoms given by E = -27.2 Z2 +16.95 Z - 4.1 For example the laboratory measurement of the ionization energy of H- yields an energy of the ground state E = - 14.35 eV In this case since Z = 1 we get E -27.2 + 16.95 - 4.1 = -14.35 eV In the same way writing for the helium Z = 2 we get E = - 108.8 + 32.9 - 4.1 = -79.0 eV which is equal to the laboratory measurement. In the same way we can calculate the ground state energies for the Z = 3 : Li+ ion , Z = 4 : Be2+ beryllium ion, and Z = 5 : B3+ boron. The discovery of this simple formula based on the well-established laws of electromagnetism was the first fundamental equation for understanding the energies of many-electron atoms, while various theories based on qualitative symmetry properties lead to complications. According to the experiments the helium ground state consists of two identical 1s electrons with a ground state energy E(He) = -79 eV. The energy ( E1) required to remove one of them is the highest ionization energy of any atom in the periodic table: E1 = 24.6 electron volts. The energy (E2) required to remove the second electron is E2 = 54.4 eV, as would be expected by modeling it after the hydrogen energy levels. According to the Bohr model (1913 ) and the well-established Schrodinger equation of the quantum mechanics (1926) the He+ ion is just like a hydrogen atom with two units of charge in the nucleus. (Z = 2). Since the hydrogenic energy levels depend upon the square of the nuclear charge, the ground state energy E (He+) in eV of the remaining helium electron or of the He+ should be given by E (He+) = (-13.6)Z2 = (-13.6)22 = -54.4 eV Therefore E2 = - E(He+) = (-54.4) = 54.4 eV as observed. However for the calculation of E1 = 24.6 eV = E (He+) - E(He) = -54.4 - (-79) So in the absence of a detailed knowledge about the electromagnetic force between the two spinning electrons of opposite spin many physicist today using wrong theories cannot explain correctly the ground state energy E(He) = -79 eV. For example under wrong theories based on qualitative approaches many physicists believe incorrectly that the second electron is less tightly bound because it could be interpreted as a shielding effect; the other electron partly shields the second electron from the full charge of the nucleus. Another wrong way to view the energy is to say that the repulsion of the electrons contributes a positive potential energy which partially offsets the negative potential energy contributed by the attractive electric force of the nuclear charge. Under such false ideas I published in Ind. J. Th. Phys. (2008) my paper “Spin-spin interactions of electrons and also of nucleons create atomic molecular and nuclear structures”. (See it in “User Kaliambos”). Category:Fundamental physics concepts